4

Determine the allowable flexural stress, Fb: Since the section is compact and the lateral unbraced length, Lb = 60 in., is less than Lc = 83.4 in., the allowable bending stress from Equation 4.28 is 0.66Fy = 24 ksi.

Determine the section modulus of the beam with cover plates:

q _ ^combination section

Sx,combination section

'23.57s

Determine flexural capacity of the beam with cover plates:

^x,combination section Sx,combination sectionFb (192)(24) 4608 k in.

Since the flexural capacity of the beam without cover plates is

the increase in flexural capacity is 68.4%.

Determine diameter and longitudinal spacing of bolts: From Mechanics of Materials, the relationship between the shear flow, q, the number of bolts per shear plane, n, the allowable bolt shear stress, Fv, the cross-sectional bolt area, Ab, and the longitudinal bolt spacing, s, at the interface of two component elements of a combination section is given by nFvAb — = q

If 2 in. diameter A325-N bolts are used, we have Ab = p(i)2/4 = 0.196 in. and Fv = 21 ksi (from Table 4.12), from which s can be solved from the above equation to be 4.57 in. However, for ease of installation, use s = 4.5 in.

In calculating the section properties of the combination section, no deduction is made for the bolt holes in the beam flanges nor the cover plates, which is allowed provided that the following condition is satisfied:

0.5FuAfn > 0.6FyAfg where Fy and Fu are the minimum specified yield strength and tensile strength, respectively. Afn is the net flange area and Afg is the gross flange area. For this problem

so the use of gross cross-sectional area to compute section properties is justified. In the event that the condition is violated, cross-sectional properties should be evaluated using an effective tension flange area Afe given by

Note: Lp given in this table are valid only if the bending coefficient Cb is equal to unity. If Cb > 1, the value of Lp can be increased. However, using the Lp expressions given above for Cb > 1 will give conservative value for the flexural design strength.

Cb is a factor that accounts for the effect of moment gradient on the lateral torsional buckling strength of the beam. Lateral torsional buckling strength increases for a steep moment gradient. The worst loading case as far as lateral torsional buckling is concerned is when the beam is subjected to a uniform moment resulting in single curvature bending. For this case Cb = 1. Therefore, the use of Cb = 1 is conservative for the design of beams.

4.5.1.2.1.3 Noncompact Section Members Bent about Their Major Axes — For Lb < Lp (flange or web local buckling)

Lp, Lr, Mp, Mr are defined as before for compact section members, and

For flange local buckling:

l = bf/2tf for I-shaped members, bf/tf for channels lp, 1r are defined in Table 4.8 For web local buckling:

in which bf is the flange width, tf is the flange thickness, hc is twice the distance from the neutral axis to the inside face of the compression flange less the fillet or corner radius, and tw is the web thickness.

For Lp < Lb < Lr (inelastic lateral torsional buckling), fbMn is given by Equation 4.40 except that the limit 0.90Mp is to be replaced by the limit 0.90M^.

For Lb > Lr (elastic lateral torsional buckling), fbMn is the same as for compact section members as given in Equation 4.41 or 4.42.

4.5.1.2.1.4 Noncompact Section Members Bent about Their Minor Axes — Regardless of the value of Lb, the limit state will be either flange or web local buckling, and f bMn is given by Equation 4.42.

4.5.1.2.1.5 Slender Element Sections — Refer to Section 4.10.

4.5.1.2.1.6 Tees and Double Angle Bent about Their Major Axes — The design flexural strength for tees and double-angle beams with flange and web slenderness ratios less than the corresponding limiting slenderness ratios 1r shown in Table 4.8 is given by fbMn = 0.90

1^/EIyGJ

where

Use the plus sign for B if the entire length of the stem along the unbraced length of the member is in tension. Otherwise, use the minus sign. b equals 1.5 for stems in tension and equals 1.0 for stems in compression. The other variables in Equation 4.46 are defined as before in Equation 4.41.

4.5.1.2.2 Shear Strength Criterion

For a satisfactory design, the design shear strength of the webs must exceed the factored shear acting on the cross-section, that is f vVn > Vu

Depending on the slenderness ratios of the webs, three limit states can be identified: shear yielding, inelastic shear buckling, and elastic shear buckling. The design shear strength that corresponds to each of these limit states are given as follows: